Mr. Hopkins’s Abstract of his Memoir on Physical Geology. 275 
be principally determined by their peculiar structure, and 
will therefore be in great measure independent of the causes 
whose effects I am investigating. The case however of the 
existence of partial and irregular lines of less resistance, re- 
garded as modifying, and not as principal causes, comes within 
the sphere of our investigations. We may now proceed to 
this point. 
. Recurring again to the simple case of a lamina, it is easily 
shown* that if a fissure in its continuous propagation through 
consecutive points meet a line of less resistance, it will be 
propagated across it without change of direction, or along it, 
according as a certain condition is or is not satisfied, this con- 
dition depending on the angle at which the fissure meets the 
line of less resistance, and the cohesive power along that line 
estimated in a direction perpendicular to it.. If this angle be 
a right angle the condition is necessarily satisfied, as it must 
be also if the angle do not deviate much from a right angle, 
unless the cohesive power just mentioned be extremely small, 
so that in such cases the line of less resistance will have no 
effect on the direction of the fissure. If the angle just men- 
tioned deviate too much from a right angle, the fissure will be 
propagated along the line of less resistance; but I have 
shownf that when this ceases to be the case it will almost im- 
mediately resume the direction determined by our equation, 
so that if these lines of less resistance exist only partially and 
irregularly, and be of limited extent, they will only produce 
partial deviations in the direction of the fissure, without very 
materially affecting its general bearing. This reasoning again 
is easily extended to the general mass. 
We shall now be able to arrive (as intimated above) at 
another and important condition respecting the constitution 
of the elevated mass, with which our equation will be strictly 
applicable to determine the direction of a fissure. Ifa single 
tension act at a point of a lamina, it is easily shown (and in 
fact is in itself sufficiently obvious,) that the resuiting fissure 
will be perpendicular to the direction of the tension, the co- 
hesive power being such as above shown (p. 274) to be consis- 
tent with the strict application of our equation. In like man- 
ner it may be easily conceived, that since all the tensions act 
in the planes of their respective laminae, whatever their hori- 
zontal directions may be, the resulting fissure, whatever may 
be its horizontal direction, must necessarily (independently 
of perturbing causes,) lie in a plane perpendicular to each 
Jamina at the points where it intersects it. Hence, then, it 
* Memoir, p. 24. + Memoir, p. 23. t Memoir, p. 14. 
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